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Question
If α,β be the roots x2+px−q=0 and γ,δ be the roots of x2+px+r=0, then (α−γ)(α−δ)(β−γ)(β−δ)=
If α,β be the roots x2+px−q=0 and γ,δ be the roots of x2+px+r=0, then (α−γ)(α−δ)(β−γ)(β−δ)=
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Solution
The correct option is C 1
α,β are roots of x2+px−q=0γ,δ are roots of x2+px+r=0⇒α+β=−p=γ+δ⇒α−γ=δ−β & α−δ=γ−β∴(α−γ)(α−δ)(β−γ)(β−γ)=(α−γ)(α−δ)−(α−δ)(−(α−γ)=1
α,β are roots of x2+px−q=0
γ,δ are roots of x2+px+r=0
⇒α+β=−p=γ+δ
⇒α−γ=δ−β & α−δ=γ−β
∴(α−γ)(α−δ)(β−γ)(β−γ)=(α−γ)(α−δ)−(α−δ)(−(α−γ)=1
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